Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.acu1)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.acu1.01

Input Form

HypergeometricPFQ[{7/4}, {-(9/2), -(23/4)}, -z] == (1/(4292771175 z^(1/4))) (Sqrt[2] ((4292771175 + 8295210000 z + 2305195200 z^2 - 1511516160 z^3 + 288529920 z^4 - 34578432 z^5 - 1966080 z^6 + 2097152 z^7) BesselJ[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-1430923725 - 857171700 z + 737906400 z^2 - 174242880 z^3 + 23331840 z^4 - 2277376 z^5 + 1835008 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-4292771175 + 3152179800 z - 898959600 z^2 + 139628160 z^3 - 16496640 z^4 + 3244032 z^5 + 524288 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]